Asked whether his partner, Valerie Trierweiler, was still the first lady of France, Hollande said personal affairs should be dealt with in private.

"Everybody in their personal lives can go through hardships. This is the case for us," he said.

"These are painful moments, but I have one principle: Private affairs are dealt with in private. This is not the place nor the time to do this."

Hollande and Trierweiler are expected next month on a state visit to the United States at the invitation of President Barack Obama and his wife, Michelle. Their itinerary includes a February 11 state dinner at the White House.

Speaking at the Elysee Palace to outline his new-year plans for the economy, Hollande said he would clarify the situation before the February trip.

The allegations, which emerged Friday, have sparked a media firestorm of a kind not usually seen in France, where privacy is closely guarded. Trierweiler was hospitalized shortly after the report appeared.

"Catastrophic scenario"

According to French national daily Le Monde, Hollande's news conference -- the first of 2014 and only his third in office -- was supposed to be a chance for the embattled leader, who has seen his popularity slump since his 2012 election, to relaunch his agenda.

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Instead, it is a "catastrophic scenario," the newspaper reported -- with him trying to deal with questions about his private life as briefly as possible and turn the focus back to economic matters.

Jean-Francois Cope, leader of the opposition UMP, told television channel France 5 over the weekend that the allegations were "disastrous for the image of the presidential office," adding that the story was dominating international media coverage of France.

Former Prime Minister Alain Juppe, also of the UMP, is quoted by CNN affiliate BFMTV as saying that "many people overseas who specialize in 'French bashing' are having a field day."

Asked if there should be moves to formalize the position of the first lady -- in contrast to the United States, the partner of the French president has no defined status -- Juppe said that might not be the solution.

"In France, we love status. We can create a status for the first lady and for the second lady as well, perhaps," he joked.

Hospitalization

Patrice Biancone, head of Trierweiler's Elysee office, told CNN on Sunday the first lady had been hospitalized since Friday. He said she "needed rest" and he hoped she would leave the hospital early this week.

"We all know why she went in after the story came out," said Biancone, clearly making the link between the revelations of the magazine and Trierweiler's hospitalization.

Hollande, 59, left his longtime common-law wife, Segolene Royal -- the mother of his four children -- for Trierweiler, 48, before the 2012 presidential election.

The two are not married but live together, and she makes official state appearances.

They met when Trierweiler was a reporter for Paris Match magazine. She still works for thepublication.

Right to privacy

Hollande did not tackle the claims in the Closer article head-on as he announced ideas to tackle unemployment and measures such as deep public spending cuts to boost economic growth, which he said had to be "as vigorous as possible."

The story has however prompted questions in French media about Hollande's right to privacy, whether his security may have been jeopardized during his alleged liaisons, and Trierweiler's future status as first lady.

Asked whether his security was jeopardized in this case, the President said, "My security is insured everywhere and all times. Privately I go around with less security. People should not worry."

Hollande has not confirmed or denied the alleged affair but has threatened legal action. A statement from his entourage Friday to news agency Agence France-Presse said Hollande "deeply condemns the attacks on the right to privacy which he has a right to like every other citizen."

A survey last month by French polling organization Ifop gave Hollande an approval rating of 22%, a rise of 2 percentage points from the previous month, when he hit a record low.

Hollande, who was elected after campaigning to put growth before austerity and introduce higher taxes on the rich, has been urged by his European partners and international institutions to be bolder with his economic reforms.

France's faltering economic performance last year, accompanied by stubbornly high unemployment figures, led to fears the second-biggest economy in the eurozone could act as a brake on the region's fragile recovery.